Elsevier

European Journal of Mechanics - B/Fluids

Volume 23, Issue 6, November–December 2004, Pages 879-898
European Journal of Mechanics - B/Fluids

Two-layer hydraulic falls over an obstacle

https://doi.org/10.1016/j.euromechflu.2004.04.003Get rights and content

Abstract

Motions in a forced channel flow of two contiguous homogeneous fluids of different constant densities and different thicknesses are considered. The total depth is finite and the upper surface is constrained to be planar (rigid lid approximation). The forcing is due to a bottom obstruction. The existence of a critical thickness ratio, obtained when the square of the thickness ratio is equal to the density ratio, leads to major differences with the one-layer case. The present study concentrates on this critical case. Moreover it is restricted to hydraulic falls, which are steady flows over an obstacle providing a transition between a subcritical and a supercritical flow. A weakly nonlinear analysis is performed. At leading order the problem reduces to a forced modified Korteweg–de Vries equation which can be integrated exactly. The weakly nonlinear results are validated by comparison with a numerical integration of the full governing equations. The numerical method is based on boundary integral equation techniques. The differences with the one-layer case are the existence of a second family of subcritical hydraulic falls when the thickness ratio is below critical, and the existence of supercritical hydraulic falls described by four parameters instead of three for all thickness ratios.

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